Everyday Math guide

How do I calculate percentage change?

Percentage change = (new − old) ÷ old × 100. Subtract the old value from the new, divide by the old value, then multiply by 100. A positive result is an increase; a negative one is a decrease. For example, 80 rising to 100 is (100 − 80) ÷ 80 × 100 = +25%, while 100 falling to 80 is −20%.

Run your own numbers with the Percentage CalculatorOpen →

The formula, step by step

Percentage change measures how much a value has moved relative to where it started. The formula is (new − old) ÷ old × 100. First find the raw difference by subtracting the old value from the new value. Then divide that difference by the old value to express the change as a proportion of the starting point. Finally multiply by 100 to turn the proportion into a percentage.

The sign of the answer tells you the direction. A positive number means the value went up (an increase), and a negative number means it went down (a decrease). You can run any pair of numbers through the Percentage Calculator to see the result without doing the arithmetic by hand.

A worked example in both directions

Say a value rises from 80 to 100. The difference is 100 − 80 = 20. Divide by the old value: 20 ÷ 80 = 0.25. Multiply by 100 and you get +25%. So going from 80 to 100 is a 25% increase.

Now reverse it: a value falls from 100 to 80. The difference is 80 − 100 = −20. Divide by the old value: −20 ÷ 100 = −0.2. Multiply by 100 and you get −20%. So the same 20-unit gap is a 20% decrease coming down, not 25%.

Why the starting value matters

The old value is the base you divide by, and it changes between the two examples above — 80 in the first case, 100 in the second. That is why an equal-sized move in raw terms produces different percentages depending on where you start.

This also means a rise followed by an equal-percentage fall does not return you to the original number. A value that gains 25% and then loses 25% lands below where it began, because the 25% loss is taken from the new, higher base. Percentage moves are not symmetric, a point that comes up whenever gains and losses are described in percentage terms.

Percentage change vs. percentage points

A common mix-up is treating percentage change the same as a change in percentage points. They are different things. If a rate moves from 5% to 7%, that is a rise of 2 percentage points — you simply subtract one percentage from the other.

But as a percentage change, going from 5% to 7% is (7 − 5) ÷ 5 × 100 = +40%. Both statements describe the same move; they just answer different questions. A figure quoted as a change can mean points or a percentage change, and the two can look very far apart.

Frequently asked questions

What is the formula for percentage change?

Percentage change = (new − old) ÷ old × 100. Subtract the old value from the new value, divide by the old value, and multiply by 100. A positive result is an increase and a negative result is a decrease.

Why isn't a 25% rise cancelled out by a 25% fall?

Because the base changes. The rise is calculated from the original value, but the fall is calculated from the new, higher value. A 25% gain followed by a 25% loss leaves you below your starting point, since the loss is taken from a larger number.

What is the difference between percentage change and percentage points?

Percentage points are a plain subtraction of two percentages: 5% to 7% is +2 points. Percentage change divides that gap by the starting value: 5% to 7% is (7 − 5) ÷ 5 × 100 = +40%. Same move, two different measures.

How do I calculate a percentage decrease?

Use the same formula: (new − old) ÷ old × 100. When the new value is smaller than the old one, the result is negative. For example, 100 down to 80 gives (80 − 100) ÷ 100 × 100 = −20%, a 20% decrease.

Sources: Math is Fun — Percentage Change.

Last reviewed July 4, 2026 · Editorial policy · This is general information, not financial advice.